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The same notion runs through most parts of philosophy, and is principally made use of to explain oar abstract ideas, and to shew how we can form an idea of a triangle, for instance, which shall neither be an isoceles nor scalenum, nor be confined to any particular length and proportion of sides.
A. Three, the same as the other. Q. Are there any other kind of isoceles triangles? A. Yes, there are right-angled and obtuse-angled. Scalene Triangle. Q. What is this? A. An acute-angled scalene triangle. Q. Why is it called an acute-angled scalene triangle? A. Because all its angles are acute, and its sides are not equal. Q. Why is it called scalene? A. Because it has all its sides unequal.
Only of late had he begun to analyze things for himself and it had been something of a shock to discover that a college education was just a beginning that beyond the campus of his alma mater spread a workaday world which scoffed at dead languages and went in for a living wage, which turned from isoceles triangles and algebraic conundrums to solve the essential problems of food and clothing and shingled roofs.
A. No; it must be either an isoceles or a scalene triangle. Square. Q. What is this? A. A square. Q. Why is it called a square? A. Because all its angles are right angles, and its sides are equal. Q. How many angles has it? A. Four angles. Q. What would it make if we draw a line from one angle to the opposite one? A. Two right-angled isoceles triangles.
And in case by any accident it should happen that this fire became extinct, as the holy lamp was at Athens under the tyranny of Aristion, and at Delphi, when that temple was burnt by the Medes, as also in the time of the Mithridatic and Roman civil war, when not only the fire was extinguished, but the altar demolished, then, afterwards, in kindling this fire again, it was esteemed an impiety to light it from common sparks or flame, or from any thing but the pure and unpolluted rays of the sun, which they usually effect by concave mirrors, of a figure formed by the revolution of an isoceles rectangular triangle, all the lines from the circumference of which meeting in a center, by holding it in the light of the sun they can collect and concentrate all its rays at this one point of convergence; where the air will now become rarefied, and any light, dry, combustible matter will kindle as soon as applied, under the effect of the rays, which here acquire the substance and active force of fire.
A. When the three sides are of the same length. Q. Have you any thing else to observe upon this? A. Yes, all its angles are acute. Isoceles Triangle. Q. What is this? A. An acute-angled isoceles triangle. Q. What does acute mean? A. When the angles are sharp. Q. Why is it called an isoceles triangle? A. Because only two of its sides are equal. Q. How many sides has it?
Q. Are there any other kind of scalene triangles? A. Yes, there is a right-angled scalene triangle, which has one right angle. Q. What else? A. An obtuse-angled scalene triangle, which has one obtuse angle. Q. Can an acute triangle be an equi-lateral triangle? A. Yes, it may be equilateral, isoceles, or scalene. Q. Can a right-angled triangle, or an obtuse-angled triangle, be an equilateral?
The farmer took from her hand the well-worn copy of Euclid's Elements, and laying aside his hat with reverence, he read aloud: "The angles at the base of an isoceles triangle are equal, and whosoever shall produce the sides, lo, the same also shall be equal each unto each." The farmer put the book aside. "It's no use, Anna. I can't read the good words to-night."
It will be seen on a map that North Natal forms a fairly regular isoceles triangle, having Charlestown, Majuba, and Laing's Nek at the apex, the Drakensberg range separating it from the Free State on the one side, and the Buffalo River with its lower hills separating it from the Transvaal on the other.
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